Author Archives: selitskaya

Kitchen Style Tutorials: Set Theory #7

Functions, embeddings, restrictions/extensions, composites, canonical mappings, inversions, in/surjections, kernels, isomorphisms… Functions are special kinds of Relations, those Relations that would not “split”. In our Tropical Island analogy that would mean that we are looking for only one best look-alike coconut … Continue reading

Posted in Mathematical Ruminations | Tagged , , , , , | Leave a comment

Kitchen Style Tutorials: Set Theory #6

Relations So far we were talking about Sets as collections of isolated objects – like Islands in the Ocean, maybe aggregating into Archipelagos, but still unconnected and unrelated to each other. That is a quite boring picture and actually unrealistic … Continue reading

Posted in Mathematical Ruminations | Tagged , , , , , | Leave a comment

Kitchen Style Tutorials: Set Theory #5

If you haven’t noticed (likely you have, just have forgiven it) we weren’t rigorous in our definition of the union of sets: ∪ = {x: x ∈ X for some X in C}, or intersection of sets ∩ = {x: x … Continue reading

Posted in Mathematical Ruminations | Tagged , , , , , | Leave a comment

Kitchen Style Tutorials: Set Theory #4

Unions and Intersections of Sets When we introduced Axiom of Specification we allowed ourselves to create new sets from the ones we can already find out there in the Universe. When we introduced Axiom of Pairing, we agreed we can … Continue reading

Posted in Mathematical Ruminations | Tagged , , , , | Leave a comment

Kitchen Style Tutorials: Set Theory #3

Sets of Sets When we introduced Axiom of Specification, consequences from that were quite drastic. We said that we may only create new sets from sets already existing out there, in the Universe, and we explicitly prohibited the existence of … Continue reading

Posted in Mathematical Ruminations | Tagged , , , , , | Leave a comment

Kitchen Style Tutorials: Set Theory #2

Sets In the Vector Space definition – “Collection of objects with a mathematical structure defined over them” – “collection” could be thought of as a thing that manifests itself only through a concept of “belonging”. Such thing, which interacts with … Continue reading

Posted in Mathematical Ruminations | Tagged , , , , , | Leave a comment

Kitchen Style Tutorials: Set Theory #1

Mathematical Space Mathematical space is a collection of objects with a structure defined over them. This definition as a whole, as well as the words used in it and their relations, may seem too vague, broad, and ambiguous. What is “object”? … Continue reading

Posted in Mathematical Ruminations | Tagged , , , , , | Leave a comment